A novel fixed point iteration process applied in solving the Caputo type fractional differential equations in Banach spaces

Godwin Amechi Okeke, Cyril Ifeanyichukwu Ugwuogor (), Rubayyi T. Alqahtani (), Melike Kaplan () and W. Eltayeb Ahmed ()
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Godwin Amechi Okeke: Functional Analysis and Optimization Research Group Laboratory (FANORG), Department of Mathematics, School of Physical Sciences, Federal University of Technology Owerri, P.M.B. 1526, Owerri, Imo State, Nigeria
Cyril Ifeanyichukwu Ugwuogor: Functional Analysis and Optimization Research Group Laboratory (FANORG), Department of Mathematics, School of Physical Sciences, Federal University of Technology Owerri, P.M.B. 1526, Owerri, Imo State, Nigeria
Rubayyi T. Alqahtani: ��,§Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh, Saudi Arabia
Melike Kaplan: ��Department of Computer Engineering, Faculty of Engineering and Architecture, Kastamonu University, Kastamonu, Türkiye
W. Eltayeb Ahmed: ��,§Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh, Saudi Arabia

International Journal of Modern Physics C (IJMPC), 2025, vol. 36, issue 01, 1-19

Abstract: We introduce the modified Picard–Ishikawa hybrid iterative scheme and establish some strong convergence results for the class of asymptotically generalized ϕ-pseudocontractive mappings in the intermediate sense in Banach spaces and approximate the fixed point of this class of mappings via the newly introduced iteration scheme. We construct some numerical examples to support our results. Furthermore, we apply the Picard–Ishikawa hybrid iteration scheme in solving the nonlinear Caputo type fractional differential equations. Our results generalize, extend and unify several existing results in literature.

Keywords: Asymptotically generalized ϕ-pseudocontractive mappings in the intermediate sense; iterative process; Banach spaces; modified Picard–Ishikawa hybrid iterative process; nonlinear Caputo type fractional differential equations (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1142/S0129183124501766

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